Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22626987 | C2 | direct (N × H) |
| 112. C2×C73 | #1338 | semidirect |
| 120. C73 | C2×#1338 | semidirect |
| 227. C2 | #22626987 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989690 | 2 |
| C2×#17989681 | 2 |
| #22626987 | 2 |
| C2×#17989637 | 2 |
| C2×#1338 | 73 |